A categorical guide to separation, compactness and perfectness.
A Certain Class Of Mappings In Topological Spaces
A chainable continuum not homeomorphic to an inverse limit on [0, 1] with only one bonding map
A characterization of almost continuity and weak continuity
It is well known that a function from a space into a space is continuous if and only if, for every set in the image of the closure of under is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets of .
A characterization of certain branched coverings as group actions
A characterization of closed maps using the Whyburn construction.
A characterization of light open mappings and the existence of group actions
A characterization of open mapping in terms of convergent sequences.
A characterization of Valdivia compact spaces.
A classification of continua and weakly confluent mappings
A construction of the Gleason space
A converse of the Arsenin–Kunugui theorem on Borel sets with σ-compact sections
Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel metric) space L onto a metric space M such that f(F) is a Borel subset of M if F is closed in L. We show that then is a set for all except countably many y ∈ M, that M is also Luzin, and that the Borel classes of the sets f(F), F closed in L, are bounded by a fixed countable ordinal. This gives a converse of the classical theorem of Arsenin and Kunugui. As a particular case we get Taĭmanov’s theorem saying that the image of...
A degree theory for almost continuous functions
A discontinuous function with a connected closed graph
A factorization theorem and its application to extremally disconnected resolutions
A few remarks on the set of finite-to-one maps of the Cantor set
A formal analogy between proximity and finite dimensionality
A generalization of normal spaces
A new class of spaces which contains the class of all normal spaces is defined and its characterization and properties are discussed.
A generalized continuity and product spaces
A Mapping Theorem on Aleph-spaces